Chapter 1: Prologue

The main actors of this book are classical theta functions and the Gaussian linking number. They were brought together by Edward Witten using a quantum field theory whose Lagrangian is the Chern-Simons functional. In this chapter we offer the reader a first encounter with theta functions, the linking number, and Witten's Chern-Simons theory. The discussion is less formal, less detailed, and less rigorous then the rest of the book, and should be read like a historical summary. We will revisit these notions later, with more rigor and detail.